1. Introduction

The fabrication and characterization of ultrathin films comprising of a few graphene layers have attracted a great deal of attention [1–8] due to their unique optical and electronic properties. The transmittance of such a film, which is often referred to as a multilayered graphene, is still high enough for a number of optoelectronic applications, while its conductivity may be much higher than that of graphene [5,6]. Nowadays such films are conventionally manufactured by chemical-vapor deposition (CVD) process, which enables growing a single and multilayered graphene on a variety of transition metals via thermal decomposition of hydrocarbons or surface segregation of carbon upon cooling from metastable carbon-metal solid solution [2–7]. The morphology and thickness of the fabricated film as well as the growth mechanism are determined by carbon solubility, the properties of the substrate material, and the CVD process conditions. For example, since polycrystalline Ni possesses a high carbon solubility and small grain size, few layered graphene is obtained over few microns regions and the number of layers is hardly controllable. In contrast, low carbon solubility and large grain size make copper an excellent substrate for growth of homogenous single-, bi- and multilayered graphene films over large substrate areas [5,6] because the mechanism of the graphene growth on copper is surface related [7]. Although graphene grown on Cu substrates possesses excellent opto-electronic properties [7], a scalable synthesis still requires a better understanding and optimization of the growth process. The major difficulty here is that the control of the film morphology and thickness (i.e. the number of graphene layers) is conventionally based on optical transmission and Raman techniques [5,6,9–12], which require the transfer of a grown graphene to a dielectric substrate. This makes controlling the growth process in situ impossible. It also makes it difficult to discover the connection between the growth conditions and graphene quality.

In this paper we demonstrate a simple approach that can be employed for estimation of the thickness of CVD grown multilayered graphene structures on a copper substrate and can be employed to control and characterize the growth process in situ. The proposed method is based on the measurement of the reflectance change of copper substrate due to graphene deposition and can be implemented using standard equipment available in most laboratories.

2. Experimental methods

Reflectivity of a metal substrate with coated with a homogeneous graphite film of the thickness h can be presented in the following form [13]:

In practice, however, the reflectivity of a bare copper substrate can differ from R₀ due to the surface roughness and also the presence of the native oxide layer. In order to examine the relative contribution of both factors we measured of the reflectance of bare copper foil in the visual spectral range. Figure 1 shows that in both blue and red parts of the visual spectrum, the measured reflectivity corresponds well to that calculated using the standard copper refractive index data [15]. This indicates that in our experimental conditions, the effect of the copper foil roughness is negligible. In the spectral range of 550-600 nm, we observed about ten percent discrepancy between the measured and calculated reflectivity. This discrepancy is probably associated with the interband transition at 571 nm from the filled d band to the unoccupied states in the p conduction band [16]. However we will demonstrate below that even in 550-600 nm spectral range, the differential reflectance measurement can be used for the characterization of graphene thickness.

 

Fig. 1 Measured (dotted line) and calculated using data from [15] (solid line) reflectance spectrum of the copper foil.

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It is worth noting that the oxidation processes, which result in the growth of a few nanometers thick layer of native cupric oxide (CuO), cuprous oxide (Cu₂O) and cupric hydroxide (Cu(OH)₂) on the air-copper interface [17,18], can also make a considerable contribution to the substrate reflectivity in the above spectral range. Moreover, since the refractive indices of CuO and Cu₂O are comparable with that of graphite [14,17,18] one may expect that few nanometers thick oxide and graphene films deposited onto copper substrate can give rise to a comparable reflectivity change.

3. Results and discussion

3.1 Effect of copper native oxide layer

In order to visualize the oxidation effect on the copper substrate reflectivity we removed the native oxide layer by etching the copper foil in acetic acid [19] and studied how reflectivity changes in time. One can observe from Fig. 2 that the oxidation of the etched Cu foil starts instantaneously and results in more than 5% reduction of reflectivity at 400 nm after one hour contact with air due to the strong absorption of Cu oxide in the blue spectral range. In contrast, at 600 nm, the reduction of the reflectance is as low as 1% after one hour, i.e. the effect of the oxide layer on copper reflectance is rather weak. Thus the thickness of the graphene layer can be estimated by comparing reflectivity of the copper substrate with and without graphene at the wavelengths longer than 500 nm. Figure 2 shows that the experimental error due to the presence of the native oxide layer can be suppressed if the reflectivity of the bare copper substrate is performed within five minutes after the oxide removal.

 

Fig. 2 Temporal evolution of the reflectance of the copper foil etched in acetic acid. One can observe that the reflectivity decreases by 3% at 400 nm and less than 1% at 600 nm during 10 min after oxide removal.

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3.2 Reflectivity of the graphene coated copper substrate

The obtained reflectivity R₀ of a bare copper substrate with no oxide layer makes it possible to establish a rather straightforward procedure for the graphene film thickness measurement. Specifically, one needs to measure the reflectivity R of the substrate coated with graphene film and to obtain the differential reflectivity ΔR/R₀. Since the film is just few nanometers thick, no interference effects occur and the differential reflectivity is proportional to the number of graphene layers. It can be shown that the ΔR/R₀ varied from 0.38% at λ = 800 nm to 1.15% at λ = 580 nm per graphene layer, i.e. it is large enough to be detected by the standard techniques. Thus the proposed method can be used for the graphene thickness measurement similarly to the conventional one based on the measurement of the transmittance of the graphene film transferred to a dielectric substrate [8]. The important difference, however, is that the proposed method does not require transferring the graphene film obtained on the copper foil to a transparent substrate and can be employed for the in situ control of the deposition process.

In order to demonstrate the proposed method we used it to measure the thickness of graphene films grown on 25 μm thick copper foil. The foil was annealed for 30 min at the temperature of 950 °C in 10 mBar hydrogen atmosphere. After that the CVD chamber was pumped down and filled by 1:1 H₂:CH₄ gas mixture. During 30 min of graphitization process the chamber was cooled down to 800 °C in H₂:CH₄ atmosphere at pressure of 10 mBar. After the process the chamber was pumped down again and cooled down in H₂ atmosphere to room temperature. Thus in contrast to the continuous flow system [4], the developed CVD technique allows us to reduce gas consumption. The bare copper substrate, which was used as a reference in differential reflectivity measurements, underwent the same process but in pure hydrogen (i. e. methane free) atmosphere. This allows us to obtain the bare and graphene coated substrates of the same optical quality and to suppress the effect of surface roughness on the differential reflectivity.

To obtain reflectivity of the bare substrate, the reference sample was immersed in acetic acid for 10 minutes in order to remove native oxide layer [18,19]. Reflectance measurement started as soon as 30 seconds after the acid wash and lasted for three minutes. This allowed us to partially suppress the effect of the of newly grown oxide layer on the reflectivity of the bare substrate. We did not observe the oxidation of the graphene-coated copper substrate.

The refelectance measurements were performed for two 2.5 × 2.5 cm² graphene coated copper substrates. The spectrum of the reflectance R was measured from ten spots for each substrate by Perkin Elmer Lambda-18 spectrophotometer with an integrating sphere. Figure 3 shows the differential reflectivity in the spectral range of 500-800 nm. Solid lines represent differential reflectivity calculated for substrates coated with 1, 2, 3 and 4 graphene layers. By comparing the measured and the calculated spectra in Fig. 3 one can conclude that the film consists of two graphene layers.

 

Fig. 3 The measured (dots) and the calculated (solid lines) differential reflectance spectra of the films comprising of 1, 2, 3 and 4 graphene layers. The experimental data at each wavelength are averaged over ten points on the substrate surface. One can observe that variation in the film thickness over substrate surface is less than one graphene layer.

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In order to verify the obtained results we etched the copper foil in ferric chloride solution, transferred the graphene film to quartz substrate and examined it using conventional Raman and transmission techniques [5,9,11]. The Raman spectrum obtained using Renishaw inVia Raman Microscope at excitation wavelength of 514 nm is shown in Fig. 4(a) . Large 2D/G Raman peaks ratio indicates a high crystalline quality of graphene, while the shape and shift of the 2D peak suggest that the film thickness is between 2 to 4 layers [9,11].

 

Fig. 4 (a) Raman spectrum of multilayer graphene film transferred to a SiO₂ substrate. Narrow G peak and a large ratio of 2D and D peaks indicate a high crystallinity of fabricated graphene. The shape and position of the 2D peak indicates that the film consists of 2-4 graphene layers [9,11]. (b) Transmittance of the graphene film transferred onto a SiO₂ substrate measured relatively to the transmittance of the bare substrate. Results of the transmittance measurements for different points of the sample are shown. Solid horizontal lines represent calculated transmittance of the graphene coated quartz substrate relatively to the transmittance of the bare substrate [20]. By comparing calculated data with than measured at 800 nm one can conclude that the film is comprised of about 2.6 layers.

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Transmittance spectrum is presented in Fig. 4(b). One can observe [20] that the average film thickness is about 2.6 layers, i.e. the difference between the results of the thickness measurements using reflectivity and transmittance techniques is about a half of a graphene layer. The origin of such a discrepancy may be two-fold. First, the discrepancy can be caused by the native oxide layer, which starts growing on etched copper foil surface of the reference sample instantaneously and can effect the obtained differential reflectivity. Second, the counting the number of layers by subtracting 1.87% of the transmittance per layer [20] may be not entirely accurate. This is because in such a case we assume that total optical losses of the fabricated CVD graphene film is N*2.3% where N is the number of layers, while the film is infinitesimally thin. In other words, we assume that the refractive index of the fabricated film along the substrate normal is equal to 1. Such an assumption is probably correct for graphene fabricated by exfoliation of HOPG, however it may be not entirely correct for CVD graphene. It has been shown [20] that the transmission change per layer depends on the finite optical thickness of the multilayer graphene. Nevertheless it is worth noting that both the reflectance (see Fig. 3) and the conventional (Fig. 4) measurement techniques produce almost the same result. This allows us to conclude that the measurement of the differential reflectance is a powerful yet simple tool to control the number of graphene layers grown on metal substrate. The uncertainty caused by the possible oxidation of the substrate can be suppressed by measuring performing reflectivity of the reference sample immediately after oxide removal or in an inert atmosphere. Alternatively this uncertainty can be avoided by quantitative measurement of the growth rate of the oxide layer and adjusting the reflectance of the reference sample accordingly.

4. Conclusion

In conclusion, we have demonstrated a technique that enables the revealing of the thickness of CVD nanographite film deposited on copper substrate by differential reflectivity measurements. We believe that our results offer a reliable yet simple thickness evaluation technique capable of characterising both mono- and multilayered graphene on metal surfaces and of controlling the growth process in situ.